Solve (5/6-7/2*1/5)div2/5

$$( \frac { 5 } { 6 } - \frac { 7 } { 2 } \times \frac { 1 } { 5 } ) \div \frac { 2 } { 5 }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Multiply \frac{7}{2} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{6}-\frac{7\times 1}{2\times 5}}{\frac{2}{5}}$$

Do the multiplications in the fraction \frac{7\times 1}{2\times 5}.

$$\frac{\frac{5}{6}-\frac{7}{10}}{\frac{2}{5}}$$

Least common multiple of 6 and 10 is 30. Convert \frac{5}{6} and \frac{7}{10} to fractions with denominator 30.

$$\frac{\frac{25}{30}-\frac{21}{30}}{\frac{2}{5}}$$

Since \frac{25}{30} and \frac{21}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25-21}{30}}{\frac{2}{5}}$$

Subtract 21 from 25 to get 4.

$$\frac{\frac{4}{30}}{\frac{2}{5}}$$

Reduce the fraction \frac{4}{30} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2}{15}}{\frac{2}{5}}$$

Divide \frac{2}{15} by \frac{2}{5} by multiplying \frac{2}{15} by the reciprocal of \frac{2}{5}.

$$\frac{2}{15}\times \frac{5}{2}$$

Multiply \frac{2}{15} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 5}{15\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5}{15}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$